[ 7 66 ] 
But his greateft mifiake, and which I know not 
how to reconcile to his ufual caution, is in the me- 
thod he gives for finding the places of the mefes for 
the feven modes. Not only is this method erroneous, 
but he gives it exprefly as the method of Ptolemey 
(49), though no fuch direction is to be found in his 
work. As I have already given Ptolemey’s method, 
in our modem terms, for the fake of brevity, from 
his tenth chapter, where it is delivered, I fhall here 
give that of Wallis, in the fame terms, that the dif- 
ference between the two may more eafily be feen. 
“ Firft pitch the Dorian, which is the middle 
tone, fuppofe in A ; rife a fourth to D, for the 
Mixolydian 5 fall a fifth to G, for the Hypolydian ; 
rife a fourth to C, for the Lydian. Then begin from 
the Dorian again, and fall a fourth to E, for the 
Hypodorian j rife a fifth to B, for the Phrygian j and 
fall a fourth to ¥#, for the Hypophrygian (50).” 
By this method, we fee the mefes of the Lydian 
and Hypolydian are brought out at c and / natural ; 
whereas, by Ptolemey’s, they come out at c& and 
f #, where I have placed them. 
This mifiake, I apprehend, the dodtor was .led 
into by the eleventh chapter of Ptolemey’s fecond 
book, where the mefes of the Lydian and Hypo- 
lydian are fettled in trite diezeugmenon and lichanos 
mefon ; which firings, in their natural fituation, in 
the Dorian mode, were tuned to c and g natural ; 
(49) Hanc autem methodum adhibet Ptolemaeus in tonis fuis 
feptem defignandis, &c. — primum omnium faca, &c. fecundo 
tonum furmt, &c. App. ad Ptol. p. 3 1 3 ^ 3H* 
(50) Ibid, p. 313. lin. uit. ufquc ad p. 315. lin. 20. 
but,. 
